D₃×#19149815 #45685485

order	33282
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#19149815
unambiguous semidirect product	C₃⋊(C₂×#19149815)

Splittings

Fitting, socle, derived	C₃×C₄₃² ⋊ C₂×C₃
Hall	C₃×#19149815 ⋊ C₂
Sylow	C₄₃² ⋊ C₃×D₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₄₃²	C₂×C₃
LCS	G ▷ C₃×C₄₃²
UCS	C₁

414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 5547

A minimal faithful permutation representation — 3 generators on 89 points:

(2,3)(5,6,8)(7,10,15)(9,13,12)(11,17,25)(14,20,22)(16,23,19)(18,27,36)(21,29,34)(24,32,31)(26,35,28)(30,39,43)(33,40,42)(37,44,38)(41,45,46)(48,49,51)(50,53,58)(52,56,55)(54,60,68)(57,63,65)(59,66,62)(61,70,79)(64,72,77)(67,75,74)(69,78,71)(73,82,86)(76,83,85)(80,87,81)(84,88,89);(1,2,3)(47,48,50,54,61,66,51,55,62,71,81,78,58,65,74,70,80,87,68,77,85,82,60,69,79,86,89,88,72,53,59,67,76,84,83,63,49,52,57,64,73,75,56);(4,5,7,11,18,23,8,12,19,28,38,35,15,22,31,27,37,44,25,34,42,39,17,26,36,43,46,45,29,10,16,24,33,41,40,20,6,9,14,21,30,32,13)

Conjugacy classes & character table

1857 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33282, 54);

D3×#19149815 #45685485